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Mutant knots with symmetry

Published online by Cambridge University Press:  01 January 2009

H. R. MORTON
H. R. MORTON*
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL. e-mail: su14@liverpool.ac.uk
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Abstract

Mutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general their m-string satellites can have different Homfly polynomials for m > 2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the directed m-string satellites of mutants share the same Homfly polynomial for m < 6 in general, and for all choices of m when the satellite is based on a cable knot pattern.

We give examples of mutants with extra symmetry whose Homfly polynomials of some 6-string satellites are different, by comparing their quantum sl(3) invariants.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 146 , Issue 1 , January 2009 , pp. 95 - 107
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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